Stable Robin solid wall boundary conditions for the Navier–Stokes equations

Abstract

In this paper we prove stability of Robin solid wall boundary conditions for the compressible Navier–Stokes equations. Applications include the no-slip boundary conditions with prescribed temperature or temperature gradient and the first order slip-flow boundary conditions. The formulation is uniform and the transitions between different boundary conditions are done by a change of parameters. We give different sharp energy estimates depending on the choice of parameters. The discretization is done using finite differences on Summation-By-Parts form with weak boundary conditions using the Simultaneous Approximation Term. We verify convergence by the method of manufactured solutions and show computations of flows ranging from no-slip to almost full slip.